Acoustics & Music Theory
why it sounds like that
Concept

Equivalent rectangular bandwidth — where it appears

The width of the ideal rectangular filter that would pass as much noise power as one of the ear's own filters at a given frequency. It is the modern replacement for the critical band and gives a narrower answer at low frequencies.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The critical band, measured in semitones. The width of the ear's frequency-analysis band at each pitch, converted from hertz into semitones. Two intervals drawn as horizontal lines cross the curves: below the crossing the interval fits inside one band and its notes are not resolved from each other, and above it they are.

A third is rougher in the bass

Consonance is usually presented as a property an interval has. It is not. The same major third is muddy two octaves below middle C and clean two octaves above it, the ratio never changed, and the frequency where it stops being muddy can be solved for.

intervals · Consonance Which harmonics of a 200 Hz note arrive one to a filter. One row per harmonic of a 200.0 Hz tone. The bar is the ear's analysis band at that harmonic on the equivalent rectangular bandwidth model, and the two small marks either side are the neighbouring harmonics. A harmonic is counted as resolved when the spacing to its neighbours, 200.0 Hz, exceeds that bandwidth, and 8 of 12 are. The third to fifth harmonics are picked out because published measurements put the pitch's dominance region there; nothing in this drawing derives that.

Which harmonics carry the pitch

A missing fundamental is inferred from a pattern, and a pattern has to be legible before it can be matched. Counting how many harmonics of a note land in separate auditory filters prices the inference — and the answer at the bottom of a bass guitar's range is none of them.

intervals · Missing fundamental

Named alongside it

The objects these essays reach for when they reach for this one.

Critical bandwidthConsonanceDominance regionHarmonic seriesMissing fundamentalPartialResidue pitchResolvabilityRoughnessSpectrum

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